﻿S28 Messrs. C. G. Darwin and R. H. Fowler on 



Since we may take any body for our thermometer by 

 which to measure the temperature scale, we may if we 

 like at once define the absolute temperature of statistical 

 theory as proportional to the pressure in a body of perfect 

 gas at coDstant volume. Now if there are P molecules in 

 volume V, it follows from almost any theory that 



P 



^=y§e kin ., .... . (3'1) 



where e^ n , is the mean kinetic energy of translation of a 

 molecule. In terms of 3 we have by (2'2) and (2*3) 



P- - 3 P 



rekin - ~ 2 log 1/S ; 

 and so we must have 



logl/3 = l/AT, $ = e-V™,. . . . (3-2) 



where k is a universal constant. 



This appeal to the properties of an ideal substance is, 

 however, not quite satisfactory. It is avoided in thei mo- 

 dynamics, where the absolute temperature is denned in 

 connexion with the Second Law. Now we wish to show 

 how our theorems lead to the laws of thermodynamics, and 

 so we must not postulate a knowledge of absolute tempe- 

 rature, but must only consider it in connexion with entropy. 

 Our development of the Second Law will not of course 

 have the complete generality for classical systems of such 

 treatment as Gibbs' (though we have later extended it 

 to his case), but still it will suffice to deal with assemblies 

 as general as those that have been used by most writers who 

 have deduced special thermodynamical conclusions from 

 statistical premises. 



§ 4. The usual presentation of Entropy. 



Entropy is usually introduced into statistical theory by 

 means of Boltzmann's Hypothesis relating it to probability. 

 This hypothesis is based in general on the fact that, on the 

 one hand, an assembly tends to get into its most probable 

 state, while, on the other, its entropy tends to increase, and 

 so a functional relation between the two may be postulated. 

 The general line of argument is somewhat as follows*: — 



We can assign the numerical value Wi for the probability 

 of the state of any assembly. If we have two such assemblies 



* Planck's classical work on Radiation Theory is a representative- 

 example of the use of the argument here quoted. 



